### Abstract

A layerwise shear deformation theory is developed to improve the accuracy of stress and strain prediction in the analysis of laminated shell structures. The in-plane displacement field is assumed using layerwise hyperbolic functions to accommodate complexity of zigzag in-plane warping and shear stress distribution. The assumed displacement field satisfies free transverse shear stress conditions on the top and the bottom surfaces of the laminate. The continuity of transverse shear stresses and in-plane displacements at interlamina surfaces is used to obtain the relations between layerwise structural variables. These relations, expressed in terms of laminate geometry and material properties, reduce the number of independent variables in the field description. Thus, the number of structural variables in the present model is independent of the number of laminae, which makes the model computationally efficient. The developed theory is implemented using finite element technique. To assess the accuracy of the present theory, the cylindrical bending of composite laminates, for which exact elasticity solutions exist, is investigated first. The correlation shows good agreement with exact solutions even for thick constructions. The cases of spherical laminated shells under point loading and uniformly distributed loading are investigated next. The results are compared with those obtained using classical laminate theory. As expected, good correlation is observed if thin constructions are used while significant deviations occur for thicker constructions. The developed two dimensional model provides an accurate and efficient framework for the analysis of laminated shell structures of arbitrary thickness.

Original language | English (US) |
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Title of host publication | 19th AIAA Applied Aerodynamics Conference |

State | Published - 2001 |

Event | 19th AIAA Applied Aerodynamics Conference 2001 - Anaheim, CA, United States Duration: Jun 11 2001 → Jun 14 2001 |

### Other

Other | 19th AIAA Applied Aerodynamics Conference 2001 |
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Country | United States |

City | Anaheim, CA |

Period | 6/11/01 → 6/14/01 |

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### ASJC Scopus subject areas

- Aerospace Engineering
- Mechanical Engineering

### Cite this

*19th AIAA Applied Aerodynamics Conference*

**An improved shear deformation theory for laminated shells Addressing transverse stress continuity.** / Zhou, Xu; Chattopadhyay, Aditi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*19th AIAA Applied Aerodynamics Conference.*19th AIAA Applied Aerodynamics Conference 2001, Anaheim, CA, United States, 6/11/01.

}

TY - GEN

T1 - An improved shear deformation theory for laminated shells Addressing transverse stress continuity

AU - Zhou, Xu

AU - Chattopadhyay, Aditi

PY - 2001

Y1 - 2001

N2 - A layerwise shear deformation theory is developed to improve the accuracy of stress and strain prediction in the analysis of laminated shell structures. The in-plane displacement field is assumed using layerwise hyperbolic functions to accommodate complexity of zigzag in-plane warping and shear stress distribution. The assumed displacement field satisfies free transverse shear stress conditions on the top and the bottom surfaces of the laminate. The continuity of transverse shear stresses and in-plane displacements at interlamina surfaces is used to obtain the relations between layerwise structural variables. These relations, expressed in terms of laminate geometry and material properties, reduce the number of independent variables in the field description. Thus, the number of structural variables in the present model is independent of the number of laminae, which makes the model computationally efficient. The developed theory is implemented using finite element technique. To assess the accuracy of the present theory, the cylindrical bending of composite laminates, for which exact elasticity solutions exist, is investigated first. The correlation shows good agreement with exact solutions even for thick constructions. The cases of spherical laminated shells under point loading and uniformly distributed loading are investigated next. The results are compared with those obtained using classical laminate theory. As expected, good correlation is observed if thin constructions are used while significant deviations occur for thicker constructions. The developed two dimensional model provides an accurate and efficient framework for the analysis of laminated shell structures of arbitrary thickness.

AB - A layerwise shear deformation theory is developed to improve the accuracy of stress and strain prediction in the analysis of laminated shell structures. The in-plane displacement field is assumed using layerwise hyperbolic functions to accommodate complexity of zigzag in-plane warping and shear stress distribution. The assumed displacement field satisfies free transverse shear stress conditions on the top and the bottom surfaces of the laminate. The continuity of transverse shear stresses and in-plane displacements at interlamina surfaces is used to obtain the relations between layerwise structural variables. These relations, expressed in terms of laminate geometry and material properties, reduce the number of independent variables in the field description. Thus, the number of structural variables in the present model is independent of the number of laminae, which makes the model computationally efficient. The developed theory is implemented using finite element technique. To assess the accuracy of the present theory, the cylindrical bending of composite laminates, for which exact elasticity solutions exist, is investigated first. The correlation shows good agreement with exact solutions even for thick constructions. The cases of spherical laminated shells under point loading and uniformly distributed loading are investigated next. The results are compared with those obtained using classical laminate theory. As expected, good correlation is observed if thin constructions are used while significant deviations occur for thicker constructions. The developed two dimensional model provides an accurate and efficient framework for the analysis of laminated shell structures of arbitrary thickness.

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M3 - Conference contribution

BT - 19th AIAA Applied Aerodynamics Conference

ER -